On a problem of Lions concerning real interpolation spaces. The quasi-Banach case

dc.contributor.authorCobos, Fernando
dc.contributor.authorCwikel, M.
dc.contributor.authorKühn, Thomas
dc.descriptionCRUE-CSIC (Acuerdos Transformativos 2022)
dc.description.abstractWe prove that, under a mild condition on a couple (A0;A1) of quasi-Banach spaces, all real interpolation spaces (A0;A1)θ,p with 0 < θ < 1 and 0 < p ≤ ∞ are different from each other. In the Banach case and for 1 ≤ p ≤ ∞ this was shown by Janson, Nilsson, Peetre and Zafran, thus solving an old problem posed by J.-L. Lions. Moreover, we give an application to certain spaces which are important objects in Operator Theory and which consist of bounded linear operators whose approximation numbers belong to Lorentz sequence spaces.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
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dc.journal.titleJournal of Mathematical Analysis and Applications
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRightsopen access
dc.subject.keywordReal interpolation
dc.subject.keywordDependence on the parameters
dc.subject.keywordSpaces of operators defined by approximation numbers.
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titleOn a problem of Lions concerning real interpolation spaces. The quasi-Banach case
dc.typejournal article
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